   SEARCH HOME Math Central Quandaries & Queries  Question from Coya, a student: write a function f(x) that converts feet to inches.Now write a function g(x) that converts yards to feet. Explain what the composite function f(g(x)) means. Then evaluate f(g(x)) for x = 3,6, and 9. Hi Coya.

I'll show you a similar problem:

Write a function f(x) that converts hours to minutes. Now write a function g(x) that converts days to hours. Explain what the composite function f(g(x)) means. Then evaluate and explain f(g(x)) for x = 7.

f(x): to convert hours to minutes, you would multiply by 60. So f(x) = 60x.

g(x): to convert days to hours, you would multiply by 24. So g(x) = 24x.

f(g(x)): working from the inside out, we are starting with an x and interpreting it as a number of days. First the inside g(x) is evaluated which converts it to hours, then this converted value is used as though it is the value of x for f(x), the outer function. So that value is converted from hours to minutes. The composite function f(g(x)) converts x days to the equivalent number of minutes.

f(g(x)) = f( 24x) = 60(24x). For x=7, this is 60(24(7)) = 10080. So 7 days (one week) is equal to 10080 minutes.

Try your question with this example as a guide.

Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.